Question

Solve for x............................

Answer 1

`x= 2+√(30)`

Explanation:

Given triangle is right angle triangle

Hypotenuse is x+6

side a= x+3

side b= x+1

apply Pythagorean theorem

`c^2= a^2 + b^2`

`(x+6)^2=(x+3)^2+(x+1)^2`

(x+6)^2 =(x+6)(x+6)= x^2+12x+36

(x+1)^2 = x^2 + 2x+1

(x+3)^2=x^2+6x+9

`x^2+12x+36=x^2 + 2x+1+x^2+6x+9`

`x^2+12x+36=2x^2+8x+10`

Subtract 2x^2 , 8x and 10 on both sides

`-x^2+4x+26=0`

now apply quadratic formula

a=-1, b= 4 and c=26

`x=(-b+-√(b^2-4ac))/(2a)`

`x=(-4+-√((4)^2-4(-1)(26)))/(2(-1))`

`x=(-4+-√(120))/(-2)`

sqrt(120)= 2sqrt(30)

`x=(-4+-2√(30))/(-2)`

make two equations and solve for x

`x=(-4+2√(30))/(-2)`

`x= 2-√(30)`

`x=(-4-2√(30))/(-2)`

`x= 2+√(30)`